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" EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 40
by Euclides - 1841 - 351 pages
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Report of Her Majesty's Civil Service Commissioners, Together ..., Volume 24

Great Britain. Civil Service Commission - 1880
...base and between the same parallels are equal to one another. Two equal triangles, ABC and DBG, are upon the same base BC and upon the same side of it ; prove that if AB be equal to AC the perimeter of ABC will be less than that of DBC. 4. If a straight...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...diagonal Equal tnanyles upon the same base, and uIton the tame side of it, art between the same paraUelt. Let the equal triangles ABC, DBC, be upon the same base BC, and upon the same side of it. The triangles ABC, DBC, are between the same parallels ; that is, if AD be joined, AD is parallel to...
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The Cambridge Examiner, Volume 4

Education, Higher - 1884
...straight line are either two right angles, or together equal to two right angles. 11. Equal triangles on the same base, and upon the same side of it, are between the same parallels. AD is parallel to BC : AC and BD meet in E : BC is produced to P, so that the triangle PEB is equal...
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The Practical Teacher, Volume 1, Issue 1

Education - 1882
...lines drawn from the vertex, one bisecting the vertical angle, the other perpendicular to the base. 2. Equal triangles upon the same base and upon the same side of it, are between the same parallels. Point out where the demonstration begins. History. 1. Explain the relations of Mary Stuart to the thrones...
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Class lessons on Euclid

Marianne Nops - 1882
...— QED PROPOSITION XL. THEORBM. Equal triangles upon equal bases in the same straight line and on the same side of it are between the same parallels. Let the equal As ABC, DEF be on equal bases BC, EF, in A p 'the same straight line BF, and on the same side of it...
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The Practical Teacher; with which is Incorporated the Practical ..., Volume 2

Joseph Hughes - Education - 1883
...the three interior angles of every triangle are together equal to two right angles. Euclid, I., 2. 3. Equal triangles upon the same base and upon the same side of it are between the same parallels. Euclid, I., 39. Algebra. MALES. I. Add together i5-0 _ ii-*), 2дг- (3- 5^), and 2- (-4 + = I-I+IA...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...&c. QED PROPOSITION 40. THEOREM. Equal triangles, on equalbases, in the same straight line, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DEF be on equal bases BC, EF, in the same straight line BF, and on the same side of it : they shall...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd ..., Volume 3

Moffatt and Paige - 1883
...equal to the triangle DE F. Therefore, triangles upon equal bases, etc. Proposition XXXIX. Theorem. Equal triangles upon the same base, and upon the same side of it, are betwee-l the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon the...
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volume 1

Euclides - 1884
...XXXVIII., that they divide the figure into four equal triangles. 87. PROPOSITION XXXIX.— THEOREM. Equal triangles upon the same base and upon the same...Let the equal triangles ABC, DBC be upon the same l>ase BC, and upon the same side of it. Then ABC and DBC shall be between the same parallels. Join...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...parallels. Let ABC and DEF be equal AS on equal bases BC and EF, in the same straight line BF, and on the same side of it, they shall be between the same parallels. Join AD. AD shall be || to BF. For if it is not, through A draw AG || to BF, meeting ED in G, [I. 31. and join GF. Then...
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